In music, an octave (Play(help·info)) is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon which has been referred to as the "basic miracle of music," the use of which is "common in most musical systems."[1] It may be derived from the harmonic series as the interval between the first and second harmonics.

The octave above an indicated note is sometimes abbreviated 8va, and the octave below 8vb. To emphasize that it is one of the perfect intervals, the octave is sometimes designated P8; the other perfect intervals, the unison, perfect fourth, and perfect fifth, are designated PU, P4, and P5.

Contents

Theory

An example of an octave, from G4 to G5

For example, if one note has a frequency of 400 Hz, the note an octave above it is at 800 Hz, and the note an octave below is at 200 Hz. The ratio of frequencies of two notes an octave apart is therefore 2:1. Further octaves of a note occur at 2n times the frequency of that note (where n is an integer), such as 2, 4, 8, 16, etc. and the reciprocal of that series. For example, 50 Hz and 400 Hz are one and two octaves away from 100 Hz because they are ½ (or 2 −1) and 4 (or 22) times the frequency, respectively. However, 300 Hz is not a whole number octave above 100 Hz, despite being a harmonic of 100 Hz.

After the unison, the octave is the simplest interval in music. The human ear tends to hear both notes as being essentially "the same", due to closely related harmonics. For this reason, notes an octave apart are given the same note name in the Western system of music notation—the name of a note an octave above A is also A. This is called octave equivalency, the assumption that pitches one or more octaves apart are musically equivalent in many ways "and that scales are uniquely defined by specifying the intervals within an octave".[3] This is similar to enharmonic equivalency, and less so transpositional equivalency and, less still, inversional equivalency, the latter of which is generally used only in counterpoint, musical set theory, or atonal theory. The conceptualization of pitch as having two dimensions, pitch height (absolute frequency) and pitch class (relative position within the octave), inherently include octave circularity.[3] Thus all C♯s, or all 1s (if C = 0), in any octave are part of the same pitch class. Octave equivalency is a part of most "advanced musical cultures", but is far from universal in "primitive" and early music.[4][5]

Monkeys experience octave equivalency, and its biological basis apparently is an octave mapping of neurons in the auditory thalamus of the mammalian brain[6] and the perception of octave equivalency in self-organizing neural networks can form through exposure to pitched notes, without any tutoring, this being derived from the acoustical structure of those notes [7]. Studies have also shown the perception of octave equivalence in rats (Blackwell & Schlosberg, 1943), human infants (Demany & Armand, 1984)[8], and musicians (Allen, 1967) but not starlings (Cynx, 1993), 4-9 year old children (Sergeant, 1983), or nonmusicians (Allen, 1967).[3]

While octaves commonly refer to the perfect octave (P8), the interval of an octave in music theory encompasses chromatic alterations within the pitch class, meaning that G♮ to G♯ (13 semitones higher) is an augmented octave (A8), and G♮ to G♭ (11 semitones higher) is a diminished octave (d8). The use of such intervals is rare, as there is frequently a more preferable enharmonic notation available, but these categories of octaves must be acknowledged in any full understanding of the role and meaning of octaves more generally in music.

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Other uses of term

As well as being used to describe the relationship between two notes, the word is also used when speaking of a range of notes that fall between a pair an octave apart. In the diatonic scale, and the other standard heptatonic scales of Western music, there are 7 notes; if one counts both ends (see Fencepost error) there are 8 notes, hence the name "octave", from the Latin octavus, from octo (meaning "eight"). Other scales may have a different number of notes covering the range of an octave, such as the chromatic scale with 12 notes or Arabic classical scale with 17, 19, or even 24 notes, but the word "octave" is still used.

In terms of playing an instrument, "octave" may also mean a special effect involving playing two notes that are an octave apart at the same time. This effect may have to be created by the musician. However, some instruments are purposely tuned or designed to produce this effect, for example, the twelve-string guitar and the octave harmonica.

Many times singers will be described as having a four-octave range or a five-octave range. This is technically a misnomer, and is described here: five-octave vocal range. It is important to remember when hearing this description that a piano has 7+1⁄3 octaves total.

Notation

An example of the same two notes expressed regularly, in an 8va bracket, and in a 15ma bracket.

The notation 8va is sometimes seen in sheet music, meaning "play this an octave higher than written." 8va stands for ottava, the Italian word for octave (note the 8 and the word 'oct'). Sometimes 8va will also be used to indicate a passage is to be played an octave lower, although the similar notation 8vb (ottava bassa) is more common. Similarly, 15ma (quindicesima) means "play two octaves higher than written" and 15mb (quindicesima bassa) means "play two octaves lower than written." Col 8 or c. 8va stands for coll'ottava and means "play the notes in the passage together with the notes in the notated octaves". Any of these directions can be cancelled with the word loco, but often a dashed line or bracket indicates the extent of the music affected.

For music-theoretical purposes (not on sheet music), octave can be abbreviated as P8 (which is an abbreviation for Perfect Eighth, the interval between 12 semitones or an octave).

From LoveToKnow 1911

OCTAVE (from Lat. octavos, eighth,
octo, eight), a period or series of eight members. In
ecclesiastical usage the octave is the eighth day after a
particular church festival, the feast day itself and the "octave"
being counted. The octave thus always falls on the same day of the
week as the festival, and any event occurring during the period is
said to be "in the octave." In music, an octave is the eighth full tone above or
below any given note. It is produced by double or half the number
of vibrations corresponding to the given note. In the interval
between a note and its octave is contained the full scale, the
octave of a note forming the starting-point of another scale of
similar intervals to the first. The interval between a note and its
octave is also called an octave. The name is also applied to an
open metal stop in an organ, and
to a flute (more usually known
as the piccolo) one octave higher in pitch than the regular flute. It is also a term
for a "parade" in fencing. The "law of octaves"
was a term applied in 1865 to a relationship among the chemical
elements enunciated by J. A. R. Newlands.

In literature an octave is a form of verse consisting of eight
iambic lines, and complete in
itself. From its use by the poets of Sicily, the recognized type of this form is
usually called the Sicilian Octave. It is distinguished from a
single stanza of ottava rima, in which
the rhyme-arrangement is
abababcc, by having only two rhymes, arranged abababab. In German
literature the octave has been used not infrequently since
1820, when Ruckert published "Sicilianen," as they are called in
German, for the first time. The word octave is also often used to
describe the eight opening lines of a sonnet, in which the rhyme-arrangement is
abbaabba, or some modification of this, but properly always on two
rhymes only.